Here we have a major problem for Disney. Purging Fox's work on the X-Men means that Marvel would have to recast every single role, which is a mighty big task. Fan-favorite actors like Patrick Stewart (Professor X), Jennifer Lawrence (Mystique), and Hugh Jackman (Wolverine) will be difficult to replace.
But Marvel has demonstrated a keen knack for finding inspired choices to fill its superheroes' shoes. Robert Downey, Jr. as Tony Stark was a brilliant gamble. Casting a morally uncompromising Captain America was particularly difficult, but after considering dozens of actors, Marvel made a savvy choice by giving Chris Evans what has become his defining role. Nobody ever expected Chris Pratt to become an A-list movie star, but Marvel saw his potential and made him the lead in Guardians of the Galaxy.
The list goes on and on. If anyone can cast a new generation of talented actors to fill the shoes of crucial mutant characters like Jean Grey, Cyclops, or Magneto, it's Marvel.
The Logan Factor
After putting in nine appearances as Wolverine, Hugh Jackman has hung up his claws, going out with a very fitting sendoff in Logan. On the one hand, merging the two universes would mean that Marvel wouldn't be able to have Wolverine, one of Marvel Comics' most popular characters. He has wide-ranging appeal, well outside of the X-Men, and served as an Avenger for years in comic books.
On the other hand, Jackman has told the media that the one and only way he'd return to the role is if he had a chance to act opposite the Avengers. Now that that's a real possibility... Jackman has done a fantastic job in the role, but he's aged out of it. He'll be 50 in less than a year. He can still take on action and adventure movies at that age (just look at 55-year-old Tom Cruise). But Logan's healing ability means that his body ages impossibly slowly. He looks young even though he's quite old. So unless Marvel decides to induct "Old Man Logan" into the Marvel Universe, Jackman can't realistically pull it off anymore. He proved this himself by playing a much older version of his character in Logan.
Take it to the bank: There is absolutely no way Marvel will bring the X-Men into the Marvel Cinematic Universe without Wolverine. He's the most popular mutant character among hundreds, and one of Marvel Comics' crown jewels. So add it to the list of reasons Marvel will reboot the X-Men: Marvel would have its very own Wolverine for the big screen, likely a 20- or 30-something actor who could keep the role for the next decade or two.
All of that said, Disney would be crazy not to leave Deadpool alone and let those movies do their own thing. With his self-aware tone and R-rated antics, the big screen's version of Deadpool (Ryan Reynolds) is only apocryphally associated with the X-Men, anyway. Admittedly, this "leave him alone" scenario would get tricky when Deadpool 2 leads to X-Force, which involves a number of other major mutant characters. Not to mention the fact that Josh Brolin would have two roles in the MCU (Cable and Thanos). But it could be sorted out.
Legion on FX should probably be left alone, too. That series has carved out a truly unique niche for itself, and isn't affected by the X-movies.
At the end of the day, all that matters is that Marvel Studios now owns the X-Men, and will undoubtedly find the right formula to turn all those mutants into the same box office gold that the Avengers have been.